Let X, Y, and Z be random variables, and let Cov(,-) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places. (a) Cov(12Y, 9X) Answer: (b) Cov(12Y +3,9X + 8Z) Answer:

Let X, Y, and Z be random variables, and let Cov(,-) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places. (a) Cov(12Y, 9X) Answer: (b) Cov(12Y +3,9X + 8Z) Answer:

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: X and Y is a gamma Random Variable with ld=2 and a l if x and r are independent exponential Random…

Q: Suppose that the bivariate random variable W = (W1,W2)™ has a Gaussian distribution on R² with zero…

A: Given that the bivariate random variable W=W1, W2T has a Gaussian distribution on ℝ2 with zero mean…

Q: Let X, Y, and Z be random variables, and let Cov(,) denote the covariance operator as usual. Suppose…

A: We want to find (1) Cov(11Y,4X)= ? (2)Cov(11Y+3, 4X+8Y)= ?

Q: Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random…

A: At first remind that Independent ⇒UncorrelatedBut, Uncorrelated…

Q: The discrete random variable X has probability mass function kx x 2,3 x+1' 2kx P(X =x) = x=4,5 x-1'…

Q: 4 Assume the PDFS of the two independent random variables X and Y are, |1, 0<x<1 e, 0<y fx (x) = and…

A: Given the pdfs of independent random variables X and Y as fXx=1 , 0≤x≤10 , else and fYy=e-y ,…

Q: Let X be a continuous random variable symmetric about Y. Let Z = 1 if X>Y OR Z = 0 if X <= Y. Find…

A: Given: Z=1 if X>Y OR Z=0 if X<=Y

Q: 5. Let Y,, Y2, ., Yn be independent, exponentially distributed random variables with mean 0/2. Show…

A: Solution

Q: 3. Let X and Y be two continuous random variables with joint pdf 4.xy, if 0 < x < 1,0 < y < 1 f(x,…

A: Dear Student, As this question has multiple parts, we are allowed to solve only the first…

Q: Suppose that a pdf for a continuous random variable Y takes the form 1 f() 1 exp 2 V2n (y – H)2 | +…

A: Solution

Q: If X and Y are two random variables, then the covariance of x+a,Y +b,where a and b are constant is…

Q: Let x1, X2, X3 be a random sample from an exponential distribution with mean 0. Consider the three…

A: Solution

Q: 2. Consider random variable X and Y with µx= 0; 0x= 3; Hy = 1; 0y= 4. Assume that X and Y have…

A: a) Consider, EZ=E2X+2Y =2EX+2EY =(2*0)+(2*1) =2

Q: Let X1, X2 be two independent random variables with the same mean EXi = µ andpossibly different…

A: Here, X1 and X2 are two independent random variables with mean µ and variance σi2, i=1, 2.The…

Q: Let X be a uniform random variable over the interval 1 to 4 and Y is exponential with a mean of 2.…

A: Given information: X~Uni(a=1,b=4) Standard deviation of X is: σX=b-a12 =4-112 =0.8660…

Q: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

Q: Let X1, X2, ..., Xn be independent random variables and Y = min{X1, X2,..., Xn}. n Fy(y) = 1 – II (1…

A: Given that X1, X2, . . . , Xn be independent random variables and Y=minX1, X2, . . . , Xn…

Q: 4. For two independent random variables such that X sin N(0, 4), Y ~ U[0, 4], Var(2X +3Y) = Var(2X -…

Q: The random variables X1,..., Xn are independent and identically distributed with probability…

A: Given information: The probability density function of the random variables X and Y is given.

Q: A random variable X is uniform from 4 to 8. A Gaussian random variable Y has mean of 10. Approximate…

A: Given: A random variable X is uniform from 4 to 8. A Gaussian random variable Y has a mean of 10.…

Q: Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected…

A: Given: A list of n stocks Stock i has expected revenue rate μi with variance σi2 for i=1,2,...,n…

Q: Suppose X1,..., X, are iid exponential random variables with mean A Let Y, < Y, < •...< Y, be order…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: Let X,Y ~ U(0, 1) be independent random variables uniformly distributed over (0, 1) and Z = X+ (a)…

A: Introduction:- We would like to estimate the value of an unobserved random variable X, given that we…

Q: Suppose the random variables X,,X2,X; have the population variance/covariance matrix: 1 -2 0 E=-2 0…

Q: Let X and Y be jointly Gaussian random variables with PDF exp { (12 + 4y² – 2x + 1) } fx,y(x, y) for…

Q: Let X1, X2,..., Xn be independent exponential random variables with mean if. For example, E(X1)=0,…

Q: X1 and X2 are independent random variables each distributed as N (0, 1). Show that the MGF of (X,-…

Q: 3) Let X₁, X₂, X, be mutually independent and identically distributed exponential random variables…

A: Given that Xi ~ E( β = 1 ) i = 1,2,3,_____,n X1,X2,____,Xn are independent and identically…

Q: Assume that the random variables X1 and X2 are bivariate normally distributed with mean µ and…

Q: The position and elevation of a survey station are given by the random vector x= x, in |X3 which X,…

A: Hi, there! since, the multiple questions are posted, we are allowing solving first question. Kindly…

Q: Let X be a uniform random variable over the interval 1 to 4 and Y is exponential with a mean of 2.…

A: Correlation Coefficient between two Random Variables: If X and Y be two random variables, then the…

Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |3(ry? + x²y), if 0 < x <…

Q: Suppose that a random vector Y' = (Y1, Y2, Y3) has a multi-normal distribution with mean vector u…

A: Additional Property of Multivariate Normal Distribution: If X~Np(μ,∑), and Y =CX , i.e., X is a…

Q: Suppose that P, and P2 are two populations having bivariate normal distributions with mean vectors…

A: Let q1 and q2 be the prior probabilities for P1 and P2. It is given that q1 and q2 are equal i.e q1…

Q: 7. Suppose X is a continuous random variable with pdf ƒ and that Y = aX + b where a and b are…

A: Introduction: A continuous random variable is a type of random variable that assumes every value…

Q: Let X, Y, and Z be random variables, and let Cov(⋅,⋅) denote the covariance operator as usual.…

A: We want to find Cov(3Y,3X) and Cov(3Y+3,3X+8Z)

Q: 11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the…

A: Given information X and Y independent continuous random variables follows uniform distribution 0 ≤…

Q: Suppose the random variables X1, X2,X, have the population variance/covariance matrix: -2 0 E=-2 5 0…

Q: . Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Here, we have, E[X] = 0 P(-3<X<2) = 1/2 Now, P(-2<X<2) = 1/2 (Since, X cannot be…

Q: Let X, Y, and Z be random variables, and let Cov(:,-) denote the covariance operator as usual.…

Q: Let X,Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X,Y) = 2,…

A: In question, Given that X, Y, Z are three random variables with mean mu and variance sigma^2. And,…

Q: . Let (y1, Y2: .-- Yn) be independent random sample from the uniform distribution on [0, 1]. (a)…

Q: Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicity copula…

A: Given: Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicity…

Q: Let X, Y, Z be the three assets, with VAR(X) = VAR(Y) = VAR(Z) = 1. Z is independent from X and Y ,…

A: Given, X, Y, and Z be three assests. Var (X) = Var (Y) = Var (Z) = 1 Z is independent from X and Y.…

Q: Suppose that X1,·, Xn are independent and identically distributed random variables such that each X;…

A: Given information: In the given scenario, X1, X2,,…, Xn, are iid (independent and identically…

Q: For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???

A: Given - Cov ( X , Y ) = -0.9 Z = 3-X

Q: .. Let X, Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X, Y) = 2,…

A: In question, Given that X, Y, Z are three random variables with mean mu and variance sigma^2. And…

Q: Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is…

A: Given data: Let X be a random variable and Y = aX + b with a ≠ 0. To show: Show that the correlation…

Question

part A and part B

Let X, Y, and Z be random variables, and let Cov(·,;) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4,
Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places.
(a) Cov(12Y, 9X)
Answer:
(b) Cov(12Y +3, 9x + 8Z)
Answer:

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X, Y, and Z be random variables, and let Cov(⋅,⋅) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places. (a) Cov(3Y, 3X) (b) Cov(3Y + 3, 3X + 8Z)
Let X and Y be random variables, and a and b be constants. a) Prove that Cov(aX, bY) = ab Cov(X,Y). b) Prove that if a > 0 and b > 0, then ρaX,bY = ρX,Y. Conclude that the correlation coefficient is unaffected by changes in units.
Let X and Y be random variables, and a and b be constants. ???? a) Show that Cov [aX,bY] = abCov [X,Y] . b) Show that if a > 0 and b > 0, then the correlation coefficient between aX and bY is the same as the correlation coefficient between X and Y . c) Is the correlation coefficient between X and Y unaffected by changes in the units of X and Y ?
Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.
For any continuous random variables X, Y , Z and any constants a, b, show the following from the definition of the covariance:
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X, Y) = 0.5. For what values of a and b such that the random variable aX + bY have mean 3 and variance 4 ?
Let X1 and X2 be two independent random variables. Suppose each Xi is exponentially distributed with parameter λi. Let Y=Min (X1, X2). A) Find the pdf of Y. B) Find E(Y). Hint: Let Y = Min (X1, X2). 1. P[Y > c] = P[Min (X1, X2) > c] = P[X1 > c, X2 > c] 2. Obtain the pdf of Y by differentiating its cdf of Y.
The joint probability mass function p(x,y) of X and Y is defined as follows: p(0,0)=0.5 p(1,0)=0.2 p(0,1)=0.2 p(1,1)=0.1 a) What is the covariance between X and Y? b) What is the correlation coefficient of X and Y? c) Are X and Y are dependent? What about are X and Y are uncorrelated?
Let X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.
Suppose the joint PMF of random variables X and Y isP(X = x, Y = y) =3/14 , if (x, y) = (−1, 1)2/14 , if (x, y) ∈ {(0, 1),(−1, 0),(0, 0)}1/14 , if (x, y) ∈ {(1, 1),(1, 0),(−1, −1),(0, −1),(1, −1)}0, otherwise(a) Find the covariance of X and Y .(b) Find the correlation of X and Y .